When an observer looks at a dog, and uses that information to comment on the color of the dog's coat, there is a chain of causation leading directly from the dog to the observer's statement about the dog. If we denote the dog by D and the statement about the dog by S(D), the causal relationship here looks like D -> S(D), with the arrow representing causation.
Suppose the observer instead looks at the dog and sees that the dog is carrying a stick in its mouth. The observer then correctly predicts that the dog will chew on the stick in the future. Let the act of chewing on the stick in the future be C. In this case, the causal relationship looks like C <- D -> S(C); the observed dog (D) causes both C and the statement S about C.
Suppose the dog in fact does not chew on the stick. C does not happen and therefore was not caused by the dog. There is still something like causality here, though; the dog might have chewed. We could draw the causal relationship like C <~ D -> S(C), where the squiggly arrow <~ indicates potential rather than actual causation.
The observer can also refer to the dog's past. The observer sees the dog is muddy, and then says the dog has been rolling in mud. With R denoting the act of rolling in mud, in this case the causal relationship is R -> D -> S(R). This simplifies to just R -> S(R); the dog's act of rolling in mud ended up causing a statement about it doing so.
What if the observer was wrong about the dog rolling in mud? Perhaps the dog is muddy because instead they swam through a marsh. Again we need a squiggly arrow: R ~> D -> S(R). Rolling in mud could have caused the dog to be muddy, but in fact did not. This can simplify to S ~> S(R).
Suppose the observer does not look at a dog, but instead reads a storybook about a dog. In the story, the dog carries a stick in its mouth. Before turning the page, the observer predicts that the dog will soon chew on the stick. What is the relationship here? If B is the book, we do clearly have a causal relationship B -> S. Reading the book caused the observer to utter the statement. But what is S about, here? Is it about a dog, which does not exist but is described in the story? Is it about the act of the dog chewing on the stick, which may or may not be described in the story? Something about this is unclear, or requires explanation; how can we refer to something that does not exist?
Or is S really about the book? In this interpretation, the observer is not really talking about a dog, as it first appears. Instead they are predicting that the book will say the dog will chew on the stick. This can be represented as B(C) ("book says chew.") Then we can draw the causal relationships the same as before: B(C) <- B -> S(B(C)), assuming the observer is right, or B(C) <~ B -> S(B(C)), assuming the observer is wrong.
Instead of reading a book, the observer might just be imagining the dog. This is not really a different situation; the book has simply been replaced with another medium, the observer's imagination. So we can have I(C) for "imagining that the dog chews," and I(C) <- I -> S(I(C)). If we allow "imagining that the dog chews" to really mean "making a final decision, in the observer's imagination, that the dog chews," then the observer can also be wrong about that. The observer could first think the dog will chew, but then consider other aspects of the imagined scenario that interfere with that (perhaps the observer imagines the dog drops the stick and starts barking, and likes that more because it makes a better story). So we could also have I(C) <~ I -> S(I(C)).
There are also mathematical statements, which are (perhaps) about abstract things that do not physically exist. But if we choose to endorse mathematical fictionalism we can treat this in the same way as we treated the book or the observer's imagination.
Must there always be some sort of causal relationship "->" or potential causal relationship "~>" between a thing, and a statement about that thing? Or are some statements totally causally disconnected from the thing they are talking about?
